From Segal's sewing to pseudo-q-traces and back
Organizers
Speaker
Bin Gui
Time
Wednesday, November 13, 2024 1:30 PM - 3:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
In 1990, Zhu proved that if V is a C2 cofinite rational VOA, then the q-traces of the vertex operators for modules of V span a modular-invariant space. These q-traces have a clear geometric meaning: they are special cases of Segal's sewing construction (≈partial contractions for conformal blocks). However, if V is C2 cofinite but irrational, Miyamoto proved in 2004 that achieving modular invariance requires generalizing q-traces to pseudo-q-traces. At first glance, pseudo-q-traces do not appear to fit within Segal's sewing framework. Did Segal miss something?
In this talk I will provide the answer: No. By suitably adjusting Segal's sewing, we can achieve a geometric interpretation of pseudo-q-traces. Our interpretation enables us to prove a conjecture by Gainutdinov-Runkel relating the spaces of torus conformal blocks to the categorical data of V-modules. This is joint work with Hao Zhang.
In this talk I will provide the answer: No. By suitably adjusting Segal's sewing, we can achieve a geometric interpretation of pseudo-q-traces. Our interpretation enables us to prove a conjecture by Gainutdinov-Runkel relating the spaces of torus conformal blocks to the categorical data of V-modules. This is joint work with Hao Zhang.
Speaker Intro
归斌现为清华大学丘成桐数学中心助理教授。本科毕业于上海交通大学。博士毕业于美国Vanderbilt University，师从Vaughan Jones。博士后工作于美国Rutgers University。
归斌的研究兴趣为顶点算子代数，以及与其相关的泛函分析与算子代数、张量范畴等问题。在顶点算子代数表示范畴的酉性（unitarity）方面、以及其与共形网（conformal nets）的表示范畴的等价性方面都首先做出系统性的研究。多篇论文发表于Communications in Mathematical Physics, Transactions of AMS, IMRN等期刊。